Accessing life insurance is not out of the question after a cancer diagnosis, but it will require some extra leg work and effort on your point. First you should check out Livestrong's nice introductory article on life insurance.

If you are still working, you can look into options through your employer for group life insurance; especially if it is near the open enrollment period.

Finally, you can always contact a broker (ask people who you know!) and see what they will do to work with you. The cost may be high, but if you have family to plan for this may outweigh the cost of the plan.